Time Series and Moving Averages
A time series is a set of data values recorded at successive, evenly spaced points in time, such as monthly sales or yearly temperatures, and it is plotted as a line graph to show trends. A moving average smooths out short-term fluctuations and seasonal variation by averaging a fixed number of consecutive data points, making the underlying trend easier to see.
Method
- Plot the time series data as a line graph with time on the horizontal axis, in order.
- Decide the length of the moving average from the pattern in the data, for example a 4-point moving average for quarterly data with 4 seasons a year.
- Calculate the first moving average by finding the mean of the first set of consecutive points.
- Find the next moving average by dropping the earliest point in the previous set and adding the next point, then finding the mean again.
- Repeat this process, sliding along the data one point at a time, to get the full sequence of moving averages.
- Plot the moving averages on the same graph and draw a trend line through them to see the underlying direction of the data.
Worked example
A cafe's quarterly ice cream sales (in tens of pounds) are: 20, 35, 50, 25, 22, 38. Calculate the first three 4-point moving averages.
- First moving average = mean of the first 4 values = (20+35+50+25)/4 = 130/4 = 32.5.
- Second moving average = mean of values 2 to 5 = (35+50+25+22)/4 = 132/4 = 33.
- Third moving average = mean of values 3 to 6 = (50+25+22+38)/4 = 135/4 = 33.75.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find the 3-point moving average of 10, 14, 18.Show answer
Answer: 14
Q2Find the 3-point moving average of 14, 18, 20.Show answer
Answer: 17.33 (2 d.p.)
Q3Find the 4-point moving average of 8, 12, 16, 20.Show answer
Answer: 14
Q4Find the 4-point moving average of 12, 16, 20, 10.Show answer
Answer: 14.5
Q5What does a moving average smooth out in seasonal data, and what does the result reveal?Show answer
Answer: It smooths out seasonal fluctuation, revealing the underlying trend.
Q6A series of 4-point moving averages is 45, 48, 52, 55. Describe the trend shown by these values.Show answer
Answer: An increasing (upward) trend over time.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
State two reasons why a business might use moving averages when analysing sales data.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A restaurant's quarterly takings (in hundreds of pounds) for 6 quarters are: 40, 55, 70, 45, 42, 58. Calculate the first three 4-point moving averages.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Quarterly electricity bills, in pounds, for a household over 5 quarters are: 80, 120, 95, 60, 90. (a) Calculate the two 4-point moving averages that can be found from this data. (b) State whether the trend is increasing or decreasing.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the time series and moving averages worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 11 of GCSE Statistics Foundation Workbook 2 and chapter 16 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
Other cuts of this worksheet:
Next topics
Not quite what you needed?
Tell us what is missing on time series and moving averages, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.